{"paper":{"title":"On a problem of S\\'ark\\\"ozy and S\\'os for multivariate linear forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Christoph Spiegel, Juanjo Ru\\'e","submitted_at":"2018-02-21T14:55:35Z","abstract_excerpt":"We prove that for pairwise co-prime numbers $k_1,\\dots,k_d \\geq 2$ there does not exist any infinite set of positive integers $A$ such that the representation function $r_A (n) = \\{ (a_1, \\dots, a_d) \\in A^d : k_1 a_1 + \\dots + k_d a_d = n \\}$ becomes constant for $n$ large enough. This result is a particular case of our main theorem, which poses a further step towards answering a question of S\\'ark\\\"ozy and S\\'os and widely extends a previous result of Cilleruelo and Ru\\'e for bivariate linear forms."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.07597","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}